The wonderfully evocative theme music heard on the US and Canadian broadcast of House is an instrumental portion of "Teardrop" by Massive Attack.
Listen to a clip 
 
Because of licensing issues, a different theme was used in New Zealand, parts of Europe and Latin America. This was an original piece, titled "House," similar in mood and tone to "Teardrop." It was composed by Scott Donaldson and Richard Nolan.

housetheme.mp3

A new theme was introduced for Season 2.

HouseSeason2Theme.mp3
 
Many thanks to the posters on the StoryPundit Politically Incorrect House MD blog for the information and clips. Thanks to Wikipedia for information on where each theme is used.